numpy.random.Generator.logistic

method

random.Generator.logistic(loc=0.0, scale=1.0, size=None)

Draw samples from a logistic distribution.

Samples are drawn from a logistic distribution with specified parameters, loc (location or mean, also median), and scale (>0).

Parameters:

locfloat or array_like of floats, optional

Parameter of the distribution. Default is 0.

scalefloat or array_like of floats, optional

Parameter of the distribution. Must be non-negative. Default is 1.

sizeint or tuple of ints, optional

Output shape. If the given shape is, e.g., (m, n, k), then m * n * k samples are drawn. If size is None (default), a single value is returned if loc and scale are both scalars. Otherwise, np.broadcast(loc, scale).size samples are drawn.

Returns:

outndarray or scalar

Drawn samples from the parameterized logistic distribution.

也參考

scipy.stats.logistic

probability density function, distribution or cumulative density function, etc.

Notes

The probability density for the Logistic distribution is

\[P(x) = \frac{e^{-(x-\mu)/s}}{s(1+e^{-(x-\mu)/s})^2},\]

where \(\mu\) = location and \(s\) = scale.

The Logistic distribution is used in Extreme Value problems where it can act as a mixture of Gumbel distributions, in Epidemiology, and by the World Chess Federation (FIDE) where it is used in the Elo ranking system, assuming the performance of each player is a logistically distributed random variable.

References

[1]

Reiss, R.-D. and Thomas M. (2001), 「Statistical Analysis of Extreme Values, from Insurance, Finance, Hydrology and Other Fields,」 Birkhauser Verlag, Basel, pp 132-133.

[2]

Weisstein, Eric W. 「Logistic Distribution.」 From MathWorld–A Wolfram Web Resource. https://mathworld.wolfram.com/LogisticDistribution.html

[3]

Wikipedia, 「Logistic-distribution」, https://en.wikipedia.org/wiki/Logistic_distribution

Examples

Try it in your browser!

Draw samples from the distribution:

>>> loc, scale = 10, 1
>>> rng = np.random.default_rng()
>>> s = rng.logistic(loc, scale, 10000)
>>> import matplotlib.pyplot as plt
>>> count, bins, _ = plt.hist(s, bins=50, label='Sampled data')

# plot sampled data against the exact distribution

>>> def logistic(x, loc, scale):
...     return np.exp((loc-x)/scale)/(scale*(1+np.exp((loc-x)/scale))**2)
>>> logistic_values  = logistic(bins, loc, scale)
>>> bin_spacing = np.mean(np.diff(bins))
>>> plt.plot(bins, logistic_values  * bin_spacing * s.size, label='Logistic PDF')
>>> plt.legend()
>>> plt.show()

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